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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1080', 'a10': [-0.9982909435256142, 0.05843964471776836], 'a2': [-0.38084101517256314, -0.9246405361881619], 'a3': [-0.9873113120936072, 0.15879664043045638], 'a4': [-0.7099202423246631, 0.7042820809432053], 'a5': [0.3261544719433878, -0.9453164869139488], 'a6': [0.5228384531415806, 0.8524317872513432], 'a7': [-0.5673915176496713, 0.8234481560482133], 'a8': [0.9215745067295166, 0.38820153083965064], 'a9': [0.9495672539760007, -0.3135634388389013], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1080', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3989', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1626', 'a^1122', 'a^888', 'a^1898', 'a^384', 'a^818', 'a^150', 'a^2244', 'a^1160', 'a^1347', 'a^2010', 'a^2072', 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'1-4729-4729.1080-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.255637696668638, 'root_number': '-0.0354152854674469839224475128566+0.999372682013701652525908142048*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2364)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.424737180221448023653735355641-0.315782777277713950282593481602*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.111214701215', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.780862845259', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.71203742455', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1080', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1080'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-4729-4729.1080-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4729-4729.1080-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.255637696668638, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.111214701215', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1080', 'Lhash_array': ['dirichlet_L_4729.1080'], 'factors': ['1-4729-4729.1080-r0-0-0'], 'label': '1-4729-4729.1080-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1080'}
Lfunction data - 1-4729-4729.1080-r0-0-0